求解一维抛物型方程的一类半隐格式及组显格式

A Class of Semi-implicit Schemes and Explicit Scheme for Solving the 1D Parabolic Equation

基于Saul’ev算法的思想,通过对古典隐格式进行改造,得到了求解一维抛物型方程的一类无条件稳定的半隐格式,其截断误差为O(τ/h+τ+τh+h2),然后由该半隐格式出发,得到了一个组显格式.最后通过数值实验验证了所提新格式的精确性和可靠性.

In this paper,a class of semi-implicit schemes for solving the one dimensional (1D) parabolic equation is derived by revising the classical implicit scheme.The truncation error of the schemes is O(τ/h+τ+τh+h2) and it is unconditionally stable.A group explicit scheme is constructed based on the semi-implicit schemes.The accuracy and the dependability of the present methods was validated by numerical experiments.